# What is the integral of sin x

## indefinite integral

#### Summary :

With the antiderivative calculator you can calculate an antiderivative online with details and calculation steps.

antiderivative online#### Description :

With the **Root function calculator** can you use the **Antiderivative of the usual functions** Calculate using the integration properties and various online calculation mechanisms.

With the antiderivative calculator you can:

- Calculate one of the antiderivatives of a polynomial
- Calculate the antiderivatives of the usual functions
- Calculating the antiderivatives of an addition of functions
- Compute the antiderivatives of a function subtraction
- Calculate the antiderivatives of a rational fraction
- Calculate antiderivatives of compound functions
- Calculating an antiderivative through partial integration
- Calculate an antiderivative using the table of common antiderivatives

### Calculate one of the antiderivatives of a polynomial online.

The function allows you to choose any **Integrate polynomial online**.

For example, to get a **Indefinite integral** the next **Polynomial** To calculate `x ^ 3 + 3x + 1`, it is necessary to enter the antiderivative (` x ^ 3 + 3x + 1; x`), after the calculation the result will be `(3 * x ^ 2) / 2 + ( x ^ 4) / 4 + x` is returned.

### Calculate the antiderivatives of the usual functions online

The **Root function calculator** is able to online everyone **Calculate antiderivatives of the usual functions**: sin, cos, tan, tan, tan, ln, exp, sh, th, sqrt (square root) and many others.

In order to get an antiderivative of the cosine function in relation to the variable x, it is necessary to enter an antiderivative (`cos (x); x`), the result sin (x) is returned after the calculation

### Integrate a number of functions online.

The integration is a linear function, with this property the computer can achieve the desired result.

To the **Calculate an antiderivative of a function sum online**, just enter the math expression that contains the sum, specify the variable, and apply the function.

For example, to calculate an antiderivative online from the sum of the following functions `cos (x) + sin (x)`, you have to enter the antiderivative (`cos (x) + sin (x); x`), after the calculation this will be Result `sin (x) -cos (x)` is output.

### Integrate a function difference online.

To get one of the **Calculate antiderivatives of a function difference**, just enter the math expression that contains the difference, specify the variable, and apply the function.

For example, to calculate an antiderivative from the difference between the following functions `cos (x) -2x` online, it is necessary to enter the antiderivative (` cos (x) -2x; x`), after the calculation the result is `sin ( x) -x ^ 2` is output.

### Integrate rational fractions online.

To the **Antiderivatives of a rational fraction**, the calculator will use its partial fraction decomposition.

For example, to find a primitive of the following rational fraction `(1 + x + x ^ 2) / x`: One must antiderivative (` (1 + x + x ^ 2) / x; x`)

### Integrate compound functions online

In order to calculate one of the antiderivatives of a function online from the form u (ax + b), where u represents a common function, it is sufficient to enter the mathematical expression that contains the function, specify the variable and apply the function.

For example, to calculate an antiderivative of the following function `exp (2x + 1)` online, you must enter antiderivative (`exp (2x + 1); x`), after the calculation the result will be` exp (2x + 1) / 2` is displayed.

For example, to calculate an antiderivative of the following function `sin (2x + 1)`, you would enter antiderivative (`sin (2x + 1); x`) to get the following result` -cos (2 * x + 1 ) / 2`.

### Integration through parts

For the calculation of certain functions, the calculator can use the **partial integration**, also "**Integration through parts**The formula used is as follows: Let f and g be two continuous functions, `int (f'g) = fg-int (fg ')`

For example, to compute an antiderivative of x⋅sin (x), the calculator uses integration by parts to get the result, it is necessary to enter antiderivative (`x * sin (x); x`), after which Calculation will return the result sin (x) -x * cos (x) with the steps and the details of the calculations.

### How do you compute an antiderivative?

Around **to compute an antiderivative**, the following formulas can be used and the usual calculation rules applied:

f (x) | F (x) |
---|---|

k | kx + c |

x | `x ^ 2/2 + c` |

`x ^ n` | `x ^ (n + 1) / (n + 1) + c` |

`1 / x ^ n` | `-1 / ((n-1) * x ^ (n-1)) + c` |

abs (x) | `x / 2` + c |

arccos (x) | `x * arccos (x) -sqrt (1- (x) ^ 2)` + c |

arcsin (x) | `x * arcsin (x) + sqrt (1- (x) ^ 2)` + c |

arctan (x) | `x * arctan (x) -1 / 2 * ln (1+ (x) ^ 2)` + c |

ch (x) | `sh (x)` + c |

cos (x) | `sin (x)` + c |

cotan (x) | `ln (sin (x))` + c |

coth (x) | `ln (sh (x))` + c |

exp (x) | `exp (x)` + c |

ln (x) | `x * ln (x) -x` + c |

log (x) | `(x * log (x) -x) / ln (10)` + c |

racine_cubique (x) | `3/4 * (x) ^ (4/3)` + c |

sh (x) | `ch (x)` + c |

sin (x) | `-cos (x)` + c |

sqrt (x) | `2/3 * (x) ^ (3/2)` + c |

tan (x) | `-ln (cos (x))` + c |

th (x) | `ln (ch (x))` + c |

**Antiderivatives array**used: c stands for a constant; F '(x) = f (x).

By applying the integration formulas and using the **Table of the usual antiderivatives** it is possible to compute many antiderivatives. These are the calculation methods the calculator uses to find the antiderivative.

With the antiderivative calculator you can calculate an antiderivative online with details and calculation steps.

#### Syntax:

antiderivative (function; variable).#### Examples:

##### Antiderivative of a trigonometric function

This example shows how to use the **Root function calculator** used to compute an antiderivative of sin (x) + x with respect to x, which must be entered:

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